FA-79741 / Barcode symbology encoding / Open access
Bar edges drift because the module width is rounded first · case 01
Symbols printed at fractional pixel pitches grow or shrink across their width and fail verification.
ROOT CAUSE
The module width is rounded to whole pixels before multiplying, so the error accumulates per module.
VERIFIED REPAIR
Round each boundary position computed from the exact fractional pitch.
Unsuccessful approach: Truncating the exact position biases every edge to the left.
Case contract
Render a module string ("1" bar, "0" space) at xn/xd device pixels per module after `quiet` leading quiet-zone modules. Module boundary k lies at round-half-up((quiet + k) * X), computed from the exact fraction so errors do not accumulate. Adjacent bar modules merge into one bar [start, end); bar width reduction shaves `bwr` pixels from the right edge of each bar, but a bar is never narrower than 1 pixel.
Why this case matters
Retail, logistics, pharmacy and document workflows depend on encoders that produce exactly the module pattern, code-set switches, separators and quiet zones scanners expect; one misplaced module or separator makes a label unreadable or, worse, scan as different data.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return (quiet + i) * math.floor(X + Fraction(1, 2))
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < n and mods[j] == '1':
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('011', 5, 2, 1, 10), [[28, 32]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('0001111', 2, 1, 0, 1), [[8, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('11111', 2, 1, 2, 3), [[6, 14]]], [('1100111001', 1, 1, 1, 10), [[10, 11], [14, 16], [19, 20]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]]], [[('1111', 9, 4, 2, 3), [[7, 14]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('0011000', 3, 1, 2, 3), [[15, 19]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('110101', 2, 1, 0, 0), [[0, 4], [6, 8], [10, 12]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011110001', 11, 5, 2, 3), [[7, 8], [11, 12], [15, 22], [31, 32]]], [('101110', 4, 3, 0, 1), [[1, 3], [4, 8]]], [('1101101001', 3, 1, 0, 3), [[9, 15], [18, 24], [27, 30], [36, 39]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('0110001110', 2, 1, 0, 10), [[22, 26], [32, 38]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('10111010100111', 5, 2, 0, 1), [[3, 5], [8, 15], [18, 20], [23, 25], [30, 38]]], [('11010', 7, 3, 0, 10), [[23, 28], [30, 33]]], [('101110001000', 9, 4, 2, 0), [[0, 1], [5, 9], [18, 19]]], [('01110000', 2, 1, 0, 3), [[8, 14]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('0', 7, 3, 0, 0), []], [('00100111', 1, 1, 0, 10), [[12, 13], [15, 18]]], [('10110', 5, 2, 0, 0), [[0, 3], [5, 10]]]], [[('0111110010101', 7, 3, 0, 10), [[26, 37], [42, 44], [47, 49], [51, 54]]], [('1', 5, 2, 0, 3), [[8, 10]]], [('0110', 7, 3, 2, 10), [[26, 28]]], [('010101111001', 2, 1, 0, 0), [[2, 4], [6, 8], [10, 18], [22, 24]]], [('011111', 2, 1, 2, 3), [[8, 16]]], [('1010110101', 2, 1, 0, 1), [[2, 4], [6, 8], [10, 14], [16, 18], [20, 22]]], [('10010101110', 2, 1, 1, 3), [[6, 7], [12, 13], [16, 17], [20, 25]]], [('011110111', 9, 4, 1, 10), [[25, 33], [36, 42]]]]]
labels = ["regression: module boundary rounding", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: module boundary rounding 0 | [[33, 38]] | [[28, 32]] | Failed |
| repair trap 1 | [[5, 6], [8, 11]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[8, 16]] | [[8, 16]] | Passed |
| control 3 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 4 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| boundary 5 | [[6, 14]] | [[6, 14]] | Passed |
| boundary 6 | [[10, 11], [14, 16], [19, 20]] | [[10, 11], [14, 16], [19, 20]] | Passed |
| control 7 | [[2, 3], [6, 14]] | [[2, 3], [7, 16]] | Failed |
SHA-256 / ca038edc91277d1bf5d919a8065faf36633e276dff14583093162ccdbbe5b9f9
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return math.floor((quiet + i) * X)
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < n and mods[j] == '1':
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('011', 5, 2, 1, 10), [[28, 32]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('0001111', 2, 1, 0, 1), [[8, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('11111', 2, 1, 2, 3), [[6, 14]]], [('1100111001', 1, 1, 1, 10), [[10, 11], [14, 16], [19, 20]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]]], [[('1111', 9, 4, 2, 3), [[7, 14]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('0011000', 3, 1, 2, 3), [[15, 19]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('110101', 2, 1, 0, 0), [[0, 4], [6, 8], [10, 12]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011110001', 11, 5, 2, 3), [[7, 8], [11, 12], [15, 22], [31, 32]]], [('101110', 4, 3, 0, 1), [[1, 3], [4, 8]]], [('1101101001', 3, 1, 0, 3), [[9, 15], [18, 24], [27, 30], [36, 39]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('0110001110', 2, 1, 0, 10), [[22, 26], [32, 38]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('10111010100111', 5, 2, 0, 1), [[3, 5], [8, 15], [18, 20], [23, 25], [30, 38]]], [('11010', 7, 3, 0, 10), [[23, 28], [30, 33]]], [('101110001000', 9, 4, 2, 0), [[0, 1], [5, 9], [18, 19]]], [('01110000', 2, 1, 0, 3), [[8, 14]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('0', 7, 3, 0, 0), []], [('00100111', 1, 1, 0, 10), [[12, 13], [15, 18]]], [('10110', 5, 2, 0, 0), [[0, 3], [5, 10]]]], [[('0111110010101', 7, 3, 0, 10), [[26, 37], [42, 44], [47, 49], [51, 54]]], [('1', 5, 2, 0, 3), [[8, 10]]], [('0110', 7, 3, 2, 10), [[26, 28]]], [('010101111001', 2, 1, 0, 0), [[2, 4], [6, 8], [10, 18], [22, 24]]], [('011111', 2, 1, 2, 3), [[8, 16]]], [('1010110101', 2, 1, 0, 1), [[2, 4], [6, 8], [10, 14], [16, 18], [20, 22]]], [('10010101110', 2, 1, 1, 3), [[6, 7], [12, 13], [16, 17], [20, 25]]], [('011110111', 9, 4, 1, 10), [[25, 33], [36, 42]]]]]
labels = ["regression: module boundary rounding", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: module boundary rounding 0 | [[27, 31]] | [[28, 32]] | Failed |
| repair trap 1 | [[6, 8], [10, 15]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[8, 16]] | [[8, 16]] | Passed |
| control 3 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 4 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| boundary 5 | [[6, 14]] | [[6, 14]] | Passed |
| boundary 6 | [[10, 11], [14, 16], [19, 20]] | [[10, 11], [14, 16], [19, 20]] | Passed |
| control 7 | [[2, 3], [6, 15]] | [[2, 3], [7, 16]] | Failed |
SHA-256 / e4dc36ff17f5030e4e0cc4c992b8f5d2d4199547f2106e73a980a25f8211332b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return math.floor((quiet + i) * X + Fraction(1, 2))
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < n and mods[j] == '1':
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('011', 5, 2, 1, 10), [[28, 32]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('0001111', 2, 1, 0, 1), [[8, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('11111', 2, 1, 2, 3), [[6, 14]]], [('1100111001', 1, 1, 1, 10), [[10, 11], [14, 16], [19, 20]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]]], [[('1111', 9, 4, 2, 3), [[7, 14]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('0011000', 3, 1, 2, 3), [[15, 19]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('110101', 2, 1, 0, 0), [[0, 4], [6, 8], [10, 12]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011110001', 11, 5, 2, 3), [[7, 8], [11, 12], [15, 22], [31, 32]]], [('101110', 4, 3, 0, 1), [[1, 3], [4, 8]]], [('1101101001', 3, 1, 0, 3), [[9, 15], [18, 24], [27, 30], [36, 39]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('0110001110', 2, 1, 0, 10), [[22, 26], [32, 38]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('10111010100111', 5, 2, 0, 1), [[3, 5], [8, 15], [18, 20], [23, 25], [30, 38]]], [('11010', 7, 3, 0, 10), [[23, 28], [30, 33]]], [('101110001000', 9, 4, 2, 0), [[0, 1], [5, 9], [18, 19]]], [('01110000', 2, 1, 0, 3), [[8, 14]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('0', 7, 3, 0, 0), []], [('00100111', 1, 1, 0, 10), [[12, 13], [15, 18]]], [('10110', 5, 2, 0, 0), [[0, 3], [5, 10]]]], [[('0111110010101', 7, 3, 0, 10), [[26, 37], [42, 44], [47, 49], [51, 54]]], [('1', 5, 2, 0, 3), [[8, 10]]], [('0110', 7, 3, 2, 10), [[26, 28]]], [('010101111001', 2, 1, 0, 0), [[2, 4], [6, 8], [10, 18], [22, 24]]], [('011111', 2, 1, 2, 3), [[8, 16]]], [('1010110101', 2, 1, 0, 1), [[2, 4], [6, 8], [10, 14], [16, 18], [20, 22]]], [('10010101110', 2, 1, 1, 3), [[6, 7], [12, 13], [16, 17], [20, 25]]], [('011110111', 9, 4, 1, 10), [[25, 33], [36, 42]]]]]
labels = ["regression: module boundary rounding", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: module boundary rounding 0 | [[28, 32]] | [[28, 32]] | Passed |
| repair trap 1 | [[7, 8], [11, 15]] | [[7, 8], [11, 15]] | Passed |
| combined fault 2 | [[8, 16]] | [[8, 16]] | Passed |
| control 3 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 4 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| boundary 5 | [[6, 14]] | [[6, 14]] | Passed |
| boundary 6 | [[10, 11], [14, 16], [19, 20]] | [[10, 11], [14, 16], [19, 20]] | Passed |
| control 7 | [[2, 3], [7, 16]] | [[2, 3], [7, 16]] | Passed |
SHA-256 / 03ff1d2d91abe98d2fb56c0abbe24d4ebd53a1267acd5eeeeeb8e69060c46a4d
Verification & scope
A deterministic bounded teaching model with a stipulated contract; it makes no claim of conformance to any published specification. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:49:47.329782+00:00.
Case digest / 5effefffa859d3c10d96191555e7fbf059be4030cb4b18d65f0d1e973ac03774